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a. Normal strain and shear strain components, Ex, Ey, &z and Yxy. b. Magnitude and orientation of the maximum shear strain, Ymax (determine the orientation in degrees, measured from given state of strains). c. Principal strain components, 81, 82, and 83. d. Orientation of the principal strain plane (determine the orientation in degrees, measured from given state of strains).

a. Normal strain and shear strain components, Ex, Ey, &z and Yxy. b. Magnitude and orientation of the maximum shear strain, Ymax (determine the orientation in degrees, measured from given state of strains). c. Principal strain components, 81, 82, and 83. d. Orientation of the principal strain plane (determine the orientation in degrees, measured from given state of strains).

Elements Of Electromagnetics
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
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A rosette consisting of 3 gages forming, respectively, angles of θa, θb and θc with the x-axis is 
attached to the free surface of machine components made of material with a given Poisson’s 
ratio v and Modulus of elasticity E as shown in Fig. 6. Take note that strain values 
given above are the gage readings and not principal strains.

25 mm 250 mm 21 45° Ait 75 mm 75 mm 1 X Fig. 6: A rosette mounted on a machine part with v = 0.3 and E = 200GPa. Gage readings are: £1 = -75 × 106 mm/mm, 82 = 300 × 106 mm/mm 83 = 250 x 10-6 mm/mm
Transcribed Image Text:25 mm 250 mm 21 45° Ait 75 mm 75 mm 1 X Fig. 6: A rosette mounted on a machine part with v = 0.3 and E = 200GPa. Gage readings are: £1 = -75 × 106 mm/mm, 82 = 300 × 106 mm/mm 83 = 250 x 10-6 mm/mm
a. Normal strain and shear strain components, Ex, Ey, &z and Xxy. b. Magnitude and orientation of the maximum shear strain, Ymax (determine the orientation in degrees, measured from given state of strains). c. Principal strain components, 81, 82, and 83. d. Orientation of the principal strain plane (determine the orientation in degrees, measured from given state of strains). e. Draw 3 dimensional Mohr diagram and indicate the points X (given state of strains), center, 8₁, 82, 83, and Ymax together with their coordinate values. Also indicate the orientation of Ymax and orientation of the principal plane (both measured from given state of strains (point X)). f. Normal stress and shear stress components, Ox, Oy, O₂ and Txy. g. Magnitude and orientation of the maximum shear stress, Tmax (determine the orientation in degrees, measured from given state of stresses). h. Principal stress components, 01, 02, and 03. i. j. Draw 3 dimensional Mohr diagram and indicate the points X (given state of stresses), center, 01, 02, 03, and Tmax together with their coordinate values. Also indicate the orientation of Tmax and orientation of the principal plane (both measured from given state of strains (point X)). Orientation of the principal stress plane (determine the orientation in degrees, measured from given state of stresses).
Transcribed Image Text:a. Normal strain and shear strain components, Ex, Ey, &z and Xxy. b. Magnitude and orientation of the maximum shear strain, Ymax (determine the orientation in degrees, measured from given state of strains). c. Principal strain components, 81, 82, and 83. d. Orientation of the principal strain plane (determine the orientation in degrees, measured from given state of strains). e. Draw 3 dimensional Mohr diagram and indicate the points X (given state of strains), center, 8₁, 82, 83, and Ymax together with their coordinate values. Also indicate the orientation of Ymax and orientation of the principal plane (both measured from given state of strains (point X)). f. Normal stress and shear stress components, Ox, Oy, O₂ and Txy. g. Magnitude and orientation of the maximum shear stress, Tmax (determine the orientation in degrees, measured from given state of stresses). h. Principal stress components, 01, 02, and 03. i. j. Draw 3 dimensional Mohr diagram and indicate the points X (given state of stresses), center, 01, 02, 03, and Tmax together with their coordinate values. Also indicate the orientation of Tmax and orientation of the principal plane (both measured from given state of strains (point X)). Orientation of the principal stress plane (determine the orientation in degrees, measured from given state of stresses).
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